Facebook blamed its outage, which kept its 3.5 billion users from accessing services such as WhatsApp, Instagram and Messenger, on a faulty configuration change.
"The daily growth rate of Telegram exceeded the norm by an order of magnitude, and we welcomed over 70 million refugees from other platforms in one day," Durov wrote on his Telegram channel.
Durov said some users in the Americas may have experienced slower speeds as millions rushed to sign up at the same time, but that the service worked as usual for the majority.
EU antitrust chief Margrethe Vestager said the outage demonstrated the repercussions of relying on just a few big players and underscored the need for more rivals.
Russia said the incident showed Moscow was right to develop its own sovereign internet platforms and social networks.
WhatsApp's nearly six-hour long outage on Monday hit trading of assets from cryptocurrencies to Russian oil, market players said, although a quick shift to alternative platforms such as Telegram limited severe disruption.